FA-6146 / Polynomial arithmetic / Open access
Polynomial value at minus one · case 01
Coefficient sum evaluates at positive one rather than negative one.
ROOT CAUSE
Coefficient sum evaluates at positive one rather than negative one.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return sum(c*(-1)**i for i,c in enumerate(coeff))
Unsuccessful approach: Alternating signs begin with negative instead of positive.
Case contract
Integer coefficients in ascending power order and integer evaluation bounds; missing high-degree coefficients are zero. Rational outputs are reduced Fraction strings; the zero-polynomial degree is -1. Polynomial value at minus one. Exact operational definition: sum(c*(-1)**i for i,c in enumerate(coeff))
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Polynomial arithmetic results depend on the stated convention.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(coeff):
return sum(coeff)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 3],)', solve(*([1, 2, 3],)), 2)
check('fixture 2: ([5],)', solve(*([5],)), 5)
check('fixture 3: ([0, 1],)', solve(*([0, 1],)), -1)
check('fixture 4: ([],)', solve(*([],)), 0)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: ([1, 2, 3],) | 6 | 2 | Failed |
| fixture 2: ([5],) | 5 | 5 | Passed |
| fixture 3: ([0, 1],) | 1 | -1 | Failed |
| fixture 4: ([],) | 0 | 0 | Passed |
SHA-256 / aaeec7f3432cbaeac5418b644c9b2fc793046235af26f041eb3208e7b538c730
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(coeff):
return sum(c*(-1)**(i+1) for i,c in enumerate(coeff))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 3],)', solve(*([1, 2, 3],)), 2)
check('fixture 2: ([5],)', solve(*([5],)), 5)
check('fixture 3: ([0, 1],)', solve(*([0, 1],)), -1)
check('fixture 4: ([],)', solve(*([],)), 0)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: ([1, 2, 3],) | -2 | 2 | Failed |
| fixture 2: ([5],) | -5 | 5 | Failed |
| fixture 3: ([0, 1],) | 1 | -1 | Failed |
| fixture 4: ([],) | 0 | 0 | Passed |
SHA-256 / 3617c5ee3384e92e09e235566805d21e10b2d6d0cd115b2d69e508120f893251
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(coeff):
return sum(c*(-1)**i for i,c in enumerate(coeff))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 3],)', solve(*([1, 2, 3],)), 2)
check('fixture 2: ([5],)', solve(*([5],)), 5)
check('fixture 3: ([0, 1],)', solve(*([0, 1],)), -1)
check('fixture 4: ([],)', solve(*([],)), 0)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: ([1, 2, 3],) | 2 | 2 | Passed |
| fixture 2: ([5],) | 5 | 5 | Passed |
| fixture 3: ([0, 1],) | -1 | -1 | Passed |
| fixture 4: ([],) | 0 | 0 | Passed |
SHA-256 / ec17339a726e6e92b92d2aa28b2c780b06f9c5edf3e19d81d10f0f1114a34a63
Verification & scope
This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:37:57.938233+00:00.
Case digest / dad3d996b699200f331cb0fd033fe8b4402689e2a0c456c95ab02b9dde370e97